Solar geoengineering governance: a dynamic framework of farsighted coalition formation

Abstract

Climate interventions with solar geoengineering could reduce climate damages if deployed in a globally coordinated regime. In the absence of such a regime, however, strategic incentives of single actors might result in detrimental outcomes. A well-known concern is that a ‘free-driver’ (Weitzman ML. A voting architecture for the governance of free-driver externalities, with application to geoengineering. Scand J Econ 2015;117:1049–68), the country with the strongest preference for cooling, might unilaterally set the global thermostat to its preferred level, thus imposing damages on others. Governance structures, i.e. more or less formal institutional arrangements between countries, could steer the decentralized geoengineering deployment towards the preferable global outcome. In this paper, we show that the coalition formation literature can make a valuable contribution to assessing the relative merit of different governance schemes. An important feature of the coalition formation literature is the sophisticated dynamic structure. A country pondering whether to leave a coalition anticipates that its departure could spark another process of disintegration among the remaining members of that coalition, which in turn may affect the assessment of whether leaving the coalition is worthwhile in the first place. This dynamic structure thus enables a more realistic picture of what coalitions are likely to form and remain stable. A second important feature of coalition formation models is wide control over the ‘rules of the game’, for instance, which agents need to consent to a transition from one coalitional arrangement to another. This control over the institutional setting allows consistently comparing and discussing various international governance arrangements.

climate change, solar geoengineering, governance, coalition formation, farsightedness, dynamic game, cooperation

INTRODUCTION

Solar geoengineering (SG) denotes technologies for reflecting solar radiation away from Earth in order to counteract climate change [1, 2]. A prominent proposal is the injection of aerosols into the stratosphere. Such global cooling can significantly reduce climate damages if appropriately deployed but could severely worsen the situation if not [2, 3]. The main concerns in this context are unilateral SG deployment and the lack of international cooperation [4–8]. Bridging the gap between potentially disadvantageous and beneficial SG deployment can be achieved by governance of SG [9–15]. Assessing the merit of different governance schemes requires predictions about how they would alter countries’ incentives to cooperate on SG deployment. Our basic assumption in this article is that countries rationally deploy SG to further their interests. As the international sphere is anarchic in the sense that no supranational body can enforce a certain use of SG, cooperation among countries is possible but needs to be in the interest of all cooperating partners [13].

In this article, we present a framework of SG coalition formation, drawing on a rich literature in economics [16–18]. This framework has two main advantages. The first advantage is the ability to represent complex dynamics of coalition formation. Existing papers on SG cooperation [19–21], rooted in a long tradition of analysing cooperation incentives for GHG abatement [22–25], model SG coalition formation as a two-stage game: in the first stage, countries decide whether to enter a treaty, i.e. commit to deploying SG in cooperation with their fellow treaty members; in the second stage, countries decide on SG deployment. According to that modelling approach, a coalition is stable if it is internally stable (no member wants to leave) and externally stable (no outsider wants to join). While insightful, this approach is static and therefore unable to capture—as we will demonstrate—important dynamics of coalition formation. More realistic contributions, in particular farsighted players anticipating ripple effects from changes to a coalition, have appeared in the general climate context [26–30]. Except for a two-player repeated game in [31], to our knowledge, the SG literature has yet to adopt that dynamic approach for analysing cooperation incentives.

The second advantage of the coalition formation framework is its flexibility. We interpret the governance of SG deployment as setting the international rules of who can use SG under what circumstances. For instance, whether treaties are irreversible or renegotiable and whether coalition membership requires consent by existing members (exclusive membership game) or not (open membership game) are easy to capture in our framework. This flexibility of the framework allows modelling a wide range of formal and informal international arrangements, thus facilitating the interdisciplinary debate about SG governance.

A DYNAMIC AND FLEXIBLE FRAMEWORK OF SG COALITION FORMATION

In this section, we give a concise description of the framework of SG coalition formation. More technical details are available in Online Appendix A. The framework rests on the vast general literature on coalition formation; see Ref. [18] for an excellent overview. There are $n$ countries and $t=\mathrm{0,1},\dots$ periods. Of central importance is the state space$X$⁠: state $x_t\in X$ describes the composition of SG coalitions at time $t$⁠. Countries in a coalition cooperatively decide on the level of SG deployment and behave non-cooperatively towards other countries (we assume all coalitions to be disjoint, such that any country can only belong to a single coalition at a time). We allow countries to differ in terms of power. In a given coalition, more powerful countries have more say in how the coalition deploys SG; more powerful countries are also more likely to initiate changes to the existing state of coalitions (see the ‘protocol’ below). The period-payoff function$u_i:X\to \mathbb{R}$ captures the payoffs of country $i$ for all possible states: payoff $u_i\left(x_t\right)$ fully summarizes the entire impact to country $i$ at time $t$ when at that time countries are organized into coalitions as described by state $x_t$⁠. The payoff function clearly rests on several assumptions about the ‘global thermostat game’ of SG deployment, such as country-specific climate damages, how SG affects the climate, the direct and indirect costs associated with SG deployment, and what level of SG coalitions choose. In ‘Illustration of the SG coalition formation framework’ section, we will develop an example with specific assumptions.

The rules of coalition formation depend on the specification of a protocol and approval committees, and the flexibility allows to model very different governance arrangements on SG deployment. In every period, the protocol randomly selects one country to be a proposer (more powerful countries have a higher chance of being selected) and describes which countries are open to receive proposals from the selected country. Reversible agreements are those where the set of potential partners is always the entire set of countries. Irreversible agreements, in contrast, can be modelled by allowing to approach only countries as potential partners that have not formed any previous coalitions during the game so far. Moreover, irreversible agreements can be temporary instead of permanently binding. In such a case, the protocol simply ceases to select any committed countries as new proposers or potential partners until their going agreements have expired.

The second key building block of the framework, approval committees, specifies which state transitions require the consent of others. The proposer must send its preferred state transition to an approval committee. The new state only realizes if the committee approves the transition (some transitions might be infeasible in the first place; in such a case, no approval committee can validate the move). The framework allows for different approval rules such as unanimity (all members of the approval committee need to consent) or a majority vote. Other interesting features, such as the renegotiation of treaties and the distinction between open membership (countries entering existing treaties at will) and exclusive membership games (existing treaty members having to approve joining countries) [24], can also be considered. The set of respondents in the approval committee can also be larger than the set of countries invited to move to a new coalition, reflecting a situation in which all countries whose treaties are affected by the proposed move need to be consulted.

For a given set of rules of the game, represented by protocol and approval committees, what coalitions might form? Countries formulate strategies, i.e. full plans of the form ‘if the state is $x$⁠, what new coalition will I propose?’ and ‘if the state is $x$ and country $j$ proposes moving to state $y$⁠, am I going to accept?’. Mixed strategies are allowed so that every country can propose and accept a transition with some probability between $0$ and $1$⁠. The strategies of all players together with the initial state $x_0$ and the protocol imply a stochastic process $P$ for the evolution of states $(x_t{)}_t$ over time. Accordingly, all countries can calculate the expected value at the initial state ${\mathrm{x}}_0$ given the stochastic process $P$⁠,

$$V_i\left(x_0\right)={\mathbb{E}}_P\sum _{t=0}^{\mathrm{\infty }}{\delta }^t{u}_i\left(x_t\right).$$

(1)

The parameter $\delta$—for simplicity assumed to be the same for all countries—controls the level of farsightedness. The higher the parameter $\delta$⁠, the more important are long-term permanent relative to short-term temporary gains. For a value of $\delta$ close to $1$⁠, countries might be willing to push their payoffs far into the future or even endure temporary losses to better position themselves for future negotiations. As usual in game theory, an equilibrium of coalition formation is a strategy profile such that no country wants to change their strategy given the strategies of others. An equilibrium may consist of a never-ending coalition formation process, continuously cycling, or settling on some specific absorbing state. An equilibrium exists under mild conditions (see Online Appendix A.5) but is not unique in general.

ILLUSTRATION OF THE SG COALITION FORMATION FRAMEWORK

This section presents a simple setting with three countries and stylized assumptions about climate change, damages, and SG to illustrate the potential of the coalition formation framework from the previous section.

Climate change, damages and SG

Consider three countries with different baseline temperatures, denoted by $W$ (warm), $T$ (temperate) and $C$ (cold). At the moment countries decide about SG, climate change has warmed all of them uniformly by $3^{\circ }\mathrm{C}$⁠. For the clarity of exposition, we assume SG is costless, has no side effects, and cooling is uniform. We can then consider the global SG level $G$ as the cooling experienced in every country. For this stylized example, we assume that climate damages only stem from (local) temperature levels. In line with [32] and as used by [21], we consider quadratic climate damages that are minimal at an ideal temperature, here ${13}^{\circ }C$⁠. As Online Appendix B.1 demonstrates, we can write country $i$’s period payoffs as a function of the global SG level $G$⁠,

$$u_i\left(G\right)=G\cdot (2{\alpha }_i-G).$$

(2)

The payoffs are highest at country $i$’s ideal SG level ${\alpha }_i$⁠. The warmer the country, the higher the ideal SG level; see Table 1. Expression (2) is normalized such that in the absence of SG, $G=0$⁠, the period payoff is zero for all countries. We can then interpret a positive period payoff as the country benefitting from SG deployment.

Table 1:

A stylized example featuring three countries with different baseline temperatures, uniform temperature increase under climate change and uniform cooling under SG. The assumption of the same ideal local temperature, consistent with [32], results in heterogeneous ideal SG levels ${\alpha }_i$⁠. All numbers in [${}^{\circ }C$].

	Country
	Warm W	Temperate T	Cold C
Baseline temperature	$21.5$	$14.0$	$11.5$
Temperature with climate change	$24.5$	$17.0$	$14.5$
Ideal local temperature	$13.0$	$13.0$	$13.0$
Ideal SG level ${\alpha }_i$	$11.5$	$4.0$	$1.5$

Specific assumptions on the coalition formation framework

We assume that all countries have the same level of farsightedness, $\delta =0.99$⁠. We also assume that they have the same power, which has two consequences. First, the protocol is uniform, i.e. in every period, each country gets to propose with probability $1/3$⁠. Second, countries in a coalition aim to implement their average ideal SG level. With only three countries, $N=3$⁠, at most one non-singleton coalition can form. Therefore, we denote the possible states of the coalition formation process as the absence of SG coalitions ( ), the two-country coalitions (TC), (WC) and (WT), and the grand coalition (WTC).

In the following, we make two assumptions on the international sphere in which SG deployment takes place. The first assumption is that every country can unilaterally leave any treaty (many international treaties explicitly allow countries to withdraw; for instance, the USA was able to withdraw from the Paris Agreement). In the language of our framework, this means that, for example, country C can suggest the transition from (WTC) to (WT), and no approval committee needs to consent. If a country leaves, the remaining members are assumed to stay at least temporarily in the treaty. In later periods, however, those remaining countries can break apart themselves, and the anticipation of the ensuing process critically shapes the incentives to leave the treaty in the first place.

The second assumption is to rule out side-payments (transfers) from one country to another in order to lure them into treaties. This implies that expression (2) fully determines country $i$’s period payoff. While side-payments indeed play a beneficial role in some international treaties, the absence of full cooperation suggests that their role is limited [33]. Therefore, ruling out side-payments is a useful starting point for illustrating the coalition formation framework.

Weak governance

We will now contrast two scenarios of SG governance. In our first scenario, ‘weak governance’, countries are free to deploy SG as they please. Panel A in Fig. 1 summarizes the relevant aspects of the equilibrium strategies in that scenario. Both T and C would prefer the grand coalition (WTC), but country W can always do better by walking out of any existing treaty and unilaterally deploying its ideal SG level ${\alpha }_W=11.5$⁠. Any other option would imply compromising with countries of lower ideal SG levels and dragging down W’s payoffs. This is directly reflected in the stochastic process as well; see panel A in Fig. 2. With probability $1/3$⁠, W is the proposer and will leave any coalition it is part of. In contrast, both T and C prefer any coalition involving W to ( ) or (TC), and therefore do not change the state whenever they are to propose. Eventually, the coalition formation process converges to the absorbing state ( ). Note that in the weak governance scenario, the state (TC) is equivalent to ( ). Irrespective of whether T and C form a coalition or not, W is free to deploy SG, and by even higher cooling, T and C would harm themselves. Therefore, all payoffs coincide in (TC) and ( ). Accordingly, the equilibrium strategy in Fig. 1 is not unique. Since all countries are indifferent between staying in (TC) and moving to ( ), there exist equilibrium strategies under which either ( ) or (TC) can be an absorbing state. Therefore, the prediction is clear: under weak international SG governance, W will deploy a high SG level, causing substantial external damage to other countries. That is a stylized representation of the free-driver concern [7]. Note that the prediction would be the same also for the more conventional, static approach: any coalition with W as a member would violate the condition of internal stability as W always prefers to leave.

Figure 1:

Summary of period payoffs and equilibrium strategy profiles under weak governance (A) and power threshold (B). Period-payoffs $u_i$⁠, cf. expression (2), and long-term expected values given strategies $V_i$⁠, cf. expression (1), are shown in red (country W), green (country T) and blue (country C) boxes. Dark and light fills represent more and less attractive constellations, respectively. An asterisk in front of the payoff indicates that the respective country is deploying SG. Every row is dedicated to a certain going state. The dark grey box on the left indicates the coalition structure and the total global SG level in that state. For every state, the light grey boxes show the proposal of the respective country in equilibrium. If that proposition needs approval by others, the countries needed for approval are indicated by small coloured boxes to the right of the proposal: solid filled if the respective country approves the proposal in equilibrium, and filled with a diagonal line if the respective country rejects the proposal.

Figure 2:

State transition probabilities under weak governance (A) and power threshold (B). The state transition probabilities directly follow from the uniform protocol (in every period, each country gets to propose with equal probability) and the equilibrium strategies shown in Fig. 1. For weak governance, the states ( ) and (TC) are equivalent as country W is free to implement its preferred SG level irrespective of the coalitional configuration of the two other countries. Accordingly, both ( ) and (TC) are potential absorbing states of the equilibrium coalition formation process. For the power threshold, the state (TC) is the unique absorbing state, and the corresponding SG level is low (the midpoint of ${\alpha }_T$ and ${\alpha }_C$⁠). Note that in the power threshold equilibrium, the warm country W would also propose a move from ( ) to (TC), despite not having any influence on the SG deployment. This is because it knows that T and C would reject any other proposals, only waiting to implement (TC) themselves. Since there is no SG in ( ), the only way for W to get to a state with positive SG deployment is by proposing (TC).

Power threshold

In the second governance scenario, we explore the case in which SG deployment requires the deploying coalition to possess at least half of the global power, a scenario considered in [19]. The underlying story could be of strict sanctions by non-deploying countries. Whether such sanction is incentive-compatible is not the question we ask here; see ‘Concluding discussion’ section. In our three-country setting with equal powers, the power threshold implies that SG deployment can only occur in a coalition of two or three countries. Other than the power threshold, the game remains exactly as above.

The resulting coalition formation game is substantially different from the weak governance scenario. Now, as panel B in Fig. 1 demonstrates, country W is willing to cooperate in order to have access to the global thermostat; the best partner is T, the country with the most similar ideal SG level. T and C, on the other hand, both prefer a coalition among themselves. Both benefit from SG, and teaming up is the least costly compromise; recall that T and C are closer in ideal SG levels than T and W.

The new institutional setting also changes the dynamics of the state transitions; see panel B in Fig. 2. Due to the power threshold, W tries to maintain any of the high-deployment states when it is the proposer. But now T and C have a more active role to play. Consider first why, given that countries are farsighted, the grand coalition (WTC) cannot be sustained, despite none of the players having profitable single-step deviations available. By moving the game from (WTC) to (WT), country C suffers high temporary losses by giving up its access to the global thermostat but knows that it will trigger a further deviation by country T from (WT) to ( ). This is because from there, the game moves directly to (TC) with relatively high payoffs for both players T and C and no further incentives to deviate. Country T has the same motive, with the transition going through (WC) instead of (WT). This cycle of disintegration and regrouping occurs because W can block a direct move from the grand coalition to (TC).

Such transitions would be lost under a static approach. In fact, all of the states (WTC), (WT), and (TC) would be equilibrium predictions if the countries weren’t farsighted. In the dynamic framework, instead of the per-period payoffs, countries rank different states in terms of their expected long-run value. They only accept transitions to a new state if it yields a higher value and only propose states where the expected value, given the probability of that state being approved, is maximized. It is also the reason why country T, if sufficiently farsighted, would in ( ) reject a proposal from W to implement (WT), although there would be a short-term improvement for both countries. In our setting, the power threshold governance in effect moves the deployment power from the free-driver to any coalition of natural partners with a high enough share of world power. Indeed, if the ideal SG level of T were higher and closer to that of W than C, the absorbing state would have been (WT) instead of (TC).

That (TC) is an absorbing state when it yields the highest possible payoff for both T and C is easy to see. However, the equilibrium strategies in Fig. 1 do not rest on this assumption. In Online Appendix D, we provide an additional example where all countries receive their highest period payoffs in different states: W in (WT), T in (WTC), and C in (TC). The strategies in panel B in Fig. 1 still constitute a valid equilibrium. Interestingly, country T would still choose to break out of the grand coalition, only in anticipation of C doing so. The reason is that by acting first, T can receive a higher cumulative payoff as the game transitions to the absorbing state (TC) via (WC) instead of (WT). The whole reason for the grand coalition (WTC) not being stable is that C would deviate in anticipation of (TC) ultimately materializing, and T would deviate in anticipation of C’s strategy.

In a second supplementary example, we consider a case where a majority approval committee can enforce state transitions instead of a full unanimity requirement. Such institutional setting can support even the grand coalition as an absorbing state. Consider the above examples where country C wants to deviate from the grand coalition, anticipating (TC) to emerge as the absorbing state. In (TC), however, T could invite (and approve) W to join the grand coalition without the need for C to approve. Since deviating from (WTC) implies heavy temporary losses for C, it no longer wishes to initiate the disbanding cycle, and the grand coalition emerges as an absorbing state. We provide further information on these examples in Supplementary Materials.

These two supplementary examples highlight that even for a simple game with just three countries, small changes in the geoengineering game or institutional setting can result in notably different equilibrium strategies. This brings to the fore the subtleties of farsighted behaviour and dynamic strategies that would be lost in a static framework.

CONCLUDING DISCUSSION

The illustrative example in the previous section is designed to demonstrate the power and subtleties of the coalition formation framework. Clearly, we have made several simplifying assumptions. First, the underlying geoengineering deployment game is deliberately simple. In the example, we only consider three stylized countries, temperature changes both from climate change and SG are uniform, climate damages are only temperature related, and SG is costless. All those simplifying assumptions can and should be replaced by more realistic modelling choices [34]. Also, note that equilibria of coalition formation are, in general, not unique. This leads to an important equilibrium selection problem in which players might try to convince others to play a certain equilibrium instead of a different one.

The second simplification was to study SG deployment in isolation, leaving aside other instruments of climate policy. Accordingly, future research can connect the coalition formation literature to the interplay of SG with mitigation [20, 35, 36] and counter-geoengineering [21, 31, 37, 38]. Also, research and development (R&D) of geoengineering capabilities has not been the focus here [39–42], but could be tackled with the same approach, thus contributing to debates about research governance [1, Ch. 5].

For our simple example, we have assumed existing governance in the background (such as weak governance and a power threshold) and looked at the formation of SG deployment coalitions within those exogenous governance boundaries. Obviously, countries negotiate around those governance rules as well. More complex models of coalition formation can put those negotiations over governance arrangements centre stage. In the spirit of the backward induction method, the result from the coalition formation game on SG deployment under specific governance arrangements, such as the two in our example in ‘Illustration of the SG coalition formation framework’ section or more sophisticated versions, will then constitute the states in the coalition formation game on SG governance. This game will allow predictions about which governance arrangements are likely to emerge.

Finally, the coalition formation framework presented in ‘A dynamic and flexible framework of SG coalition formation’ section can be further extended. We here mention only two aspects, transfers and history dependence. Transfers between countries could easily be included in the dynamic coalition formation game, with interesting impacts on efficiency and transition dynamics [43]. History dependence, as opposed to the Markovian assumption used here, would allow to let a country’s strategy to also depend on the history of the negotiation process, e.g. reject a treaty proposal in a given state a few times before accepting it.

SUPPLEMENTARY DATA

Supplementary data are available at Oxford Open Climate Change online.

ACKNOWLEDGEMENTS

We thank Antoine Bommier, two anonymous referees, and the associate editor for constructive and helpful comments.

APC FUNDING

Waived.

CONFLICT OF INTEREST

The authors declare no conflicts of interest.

AUTHORS’ CONTRIBUTIONS

D.H. conceptualized the research. D.H. and J.L. contributed equally to the investigation and the formal analysis. J.L. wrote the code and conducted the computational analysis. D.H. and J.L. contributed equally to writing, reviewing and editing of the article and both approved the submitted version.

DATA AVAILABILITY

Code to replicate all numerical results is available at github.com/jlehtomaa/OOCC_2021.